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MATH V1101x or y Calculus I 3 pts. Prerequisites: see Courses for First-Year Students. Functions, limits, derivatives, introduction to integrals. The Help Room on the 3rd floor of Milbank Hall (Barnard College) is open during the day, Monday through Friday, to students seeking individual help from the instructors and teaching assistants. (SC)

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V1101
MATH
1101
76496
001
MW 9:10a - 10:25a
207 Mathematics Building
W 9:00a - 12:00p
207 Mathematics Building
F. Nironi 50 / 100 [ More Info ]
MATH
1101
86779
002
MW 11:00a - 12:15p
209 Havemeyer Hall
M 9:00a - 12:00p
209 Havemeyer Hall
O. Munteanu 72 / 100 [ More Info ]
MATH
1101
11046
003
MW 1:10p - 2:25p
312 Mathematics Building
E. Schertzer 64 / 100 [ More Info ]
MATH
1101
13546
004
MW 1:10p - 2:25p
207 Mathematics Building
S. Cautis 76 / 100 [ More Info ]
MATH
1101
16798
005
MW 2:40p - 3:55p
312 Mathematics Building
W 1:10p - 4:00p
312 Mathematics Building
S. Cautis 55 / 100 [ More Info ]
MATH
1101
18246
006
MW 4:10p - 5:25p
417 Mathematics Building
A. Rizzardo 27 / 35 [ More Info ]
MATH
1101
22699
007
MW 6:10p - 7:25p
520 Mathematics Building
M 7:10p - 10:00p
520 Mathematics Building
A. Levy 13 / 30 [ More Info ]
MATH
1101
28046
008
TuTh 9:10a - 10:25a
312 Mathematics Building
Th 9:00a - 12:00p
312 Mathematics Buildi
V. Pilloni 62 / 100 [ More Info ]
MATH
1101
40942
009
TuTh 1:10p - 2:25p
520 Mathematics Building
L. Piechnik 42 / 30 [ More Info ]
MATH
1101
53779
010
TuTh 2:40p - 3:55p
312 Mathematics Building
Th 1:10p - 4:00p
312 Mathematics Building
P. Horn 94 / 100 [ More Info ]
MATH
1101
60279
011
TuTh 4:10p - 5:25p
520 Mathematics Building
R. Zarev 24 / 35 [ More Info ]
MATH
1101
40998
012
TuTh 6:10p - 7:25p
203 Mathematics Building
Tu 7:10p - 10:00p
203 Mathematics Buildin
A. Gilmore 33 / 35 [ More Info ]
Spring 2010 :: MATH V1101
MATH
1101
81146
001
MW 4:10p - 5:25p
417 Mathematics Building
L. Martinez 30 / 30 [ More Info ]
MATH
1101
88247
002
TuTh 1:10p - 2:25p
203 Mathematics Building
L. Huang 45 / 100 [ More Info ]
MATH
1101
96398
003
TuTh 4:10p - 5:25p
312 Mathematics Building
L. Huang 16 / 100 [ More Info ]
MATH
1101
97646
004
TuTh 6:10p - 7:25p
203 Mathematics Building
E. Stein 80 / 100 [ More Info ]

MATH V1102x or y Calculus II 3 pts. Prerequisites: MATH V1101 or the equivalent. Methods of integration, applications of the integral, Taylor's theorem, infinite series. (SC)

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V1102
MATH
1102
48198
001
MW 11:00a - 12:15p
417 Mathematics Building
M 9:00a - 12:00p
417 Mathematics Building
A. Obus 54 / 64 [ More Info ]
MATH
1102
51047
002
MW 2:40p - 3:55p
417 Mathematics Building
W 1:10p - 4:00p
417 Mathematics Building
A. Obus 45 / 64 [ More Info ]
MATH
1102
52947
003
MW 4:10p - 5:25p
203 Mathematics Building
P. Gallagher 59 / 100 [ More Info ]
MATH
1102
57448
004
MW 6:10p - 7:25p
203 Mathematics Building
M 7:10p - 10:00p
203 Mathematics Building
Y. Liu 7 / 30 [ More Info ]
MATH
1102
61496
005
TuTh 9:10a - 10:25a
203 Mathematics Building
Th 9:00a - 12:00p
203 Mathematics Buildi
P. Horn 53 / 100 [ More Info ]
MATH
1102
04208
006
TuTh 1:10p - 2:25p
409 Barnard Hall
D. De Silva 49 / 60 [ More Info ]
MATH
1102
01006
007
TuTh 2:40p - 3:55p
409 Barnard Hall
Th 1:10p - 4:00p
409 Barnard Hall
D. De Silva 60 / 60 [ More Info ]
MATH
1102
70896
008
TuTh 6:10p - 7:25p
520 Mathematics Building
Tu 7:10p - 10:00p
520 Mathematics Buildin
H. Sultan 11 / 18 [ More Info ]
Spring 2010 :: MATH V1102
MATH
1102
27896
001
MW 1:10p - 2:25p
417 Mathematics Building
A. Knapp 28 / 64 [ More Info ]
MATH
1102
94259
002
MW 6:10p - 7:25p
520 Mathematics Building
J. Wang 30 / 30 [ More Info ]
MATH
1102
62530
003
TuTh 1:10p - 2:25p
312 Mathematics Building
O. Munteanu 47 / 100 [ More Info ]
MATH
1102
79281
004
TuTh 2:40p - 3:55p
207 Mathematics Building
O. Munteanu 26 / 100 [ More Info ]
MATH
1102
89532
005
TuTh 4:10p - 5:25p
520 Mathematics Building
A. Rizzardo 29 / 30 [ More Info ]

MATH V1201x or y Calculus III 3 pts. Prerequisites: MATH V1101 with a grade of B or better or Math V1102, or the equivalent. Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramer's rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V1201
MATH
1201
72946
001
MW 9:10a - 10:25a
312 Mathematics Building
W 9:00a - 12:00p
312 Mathematics Building
N. Le 97 / 100 [ More Info ]
MATH
1201
82097
002
MW 11:00a - 12:15p
409 Barnard Hall
M 9:00a - 12:00p
409 Barnard Hall
J. Greene 56 / 60 [ More Info ]
MATH
1201
83148
003
MW 4:10p - 5:25p
312 Mathematics Building
T. Jorgensen 53 / 70 [ More Info ]
MATH
1201
87896
004
MW 6:10p - 7:25p
420 Pupin Laboratories
M 7:10p - 10:00p
312 Mathematics Building
T. Jorgensen 33 / 70 [ More Info ]
MATH
1201
27048
005
TuTh 9:10a - 10:25a
633 Seeley W. Mudd Building
Th 9:00a - 12:00p
633 Seeley W. Mudd
G. Szekelyhidi 20 / 75 [ More Info ]
MATH
1201
29530
006
TuTh 1:10p - 2:25p
207 Mathematics Building
R. Lipshitz 98 / 100 [ More Info ]
MATH
1201
59693
007
TuTh 2:40p - 3:55p
207 Mathematics Building
Th 1:10p - 4:00p
207 Mathematics Building
A. Lauda 98 / 100 [ More Info ]
MATH
1201
59781
008
TuTh 4:10p - 5:25p
207 Mathematics Building
A. Lauda 81 / 100 [ More Info ]
MATH
1201
67198
009
MW 2:40p - 3:55p
207 Mathematics Building
W 1:10p - 4:00p
207 Mathematics Building
J. Greene 53 / 100 [ More Info ]
Spring 2010 :: MATH V1201
MATH
1201
27030
001
MW 9:10a - 10:25a
207 Mathematics Building
M. Fedorchuk 100 / 100 [ More Info ]
MATH
1201
60822
002
MW 11:00a - 12:15p
203 Mathematics Building
G. Szekelyhidi 35 / 100 [ More Info ]
MATH
1201
29570
003
MW 1:10p - 2:25p
203 Mathematics Building
G. Szekelyhidi 56 / 70 [ More Info ]
MATH
1201
75030
004
MW 2:40p - 3:55p
312 Mathematics Building
N. Le 100 / 100 [ More Info ]
MATH
1201
84780
005
MW 4:10p - 5:25p
312 Mathematics Building
T. Jorgensen 54 / 70 [ More Info ]
MATH
1201
75941
006
TuTh 11:00a - 12:15p
312 Mathematics Building
W. Zheng 21 / 110 [ More Info ]
MATH
1201
14029
007
TuTh 2:40p - 3:55p
203 Mathematics Building
F. Nironi 62 / 100 [ More Info ]
MATH
1201
27193
008
TuTh 4:10p - 5:25p
207 Mathematics Building
F. Nironi 27 / 100 [ More Info ]

MATH V1202x or y Calculus IV 3 pts. Prerequisites: MATHV1102, V1201, or the equivalent. Multiple integrals, Taylor's formula in several variables, line and surface integrals, calculus of vector fields, Fourier series. (SC)

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V1202
MATH
1202
42446
001
MW 1:10p - 2:25p
417 Mathematics Building
J. Johns 35 / 64 [ More Info ]
MATH
1202
46696
002
TuTh 1:10p - 2:25p
203 Mathematics Building
R. Friedman 77 / 100 [ More Info ]
Spring 2010 :: MATH V1202
MATH
1202
61647
001
MW 9:10a - 10:25a
203 Mathematics Building
O. Savin 59 / 100 [ More Info ]
MATH
1202
66246
002
MW 2:40p - 3:55p
203 Mathematics Building
R. Friedman 100 / 100 [ More Info ]
MATH
1202
72246
003
TuTh 1:10p - 2:25p
520 Mathematics Building
V. Tosatti 49 / 50 [ More Info ]
MATH
1202
73596
004
TuTh 11:00a - 12:15p
417 Mathematics Building
V. Tosatti 41 / 64 [ More Info ]

MATH V1207x-V1208y Honors Mathematics A-B 4 pts. Prerequisites: (see Courses for First-Year Students). The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC) Recitation Section Required.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V1207
MATH
1207
68047
001
MW 2:40p - 3:55p
203 Mathematics Building
W 1:10p - 4:00p
203 Mathematics Building
M. Thaddeus 57 / 100 [ More Info ]
Spring 2010 :: MATH V1208
MATH
1208
23396
001
MW 2:40p - 3:55p
417 Mathematics Building
M. Thaddeus 48 / 64 [ More Info ]

MATH V2000x An Introduction to higher Mathematics 3 pts. Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V2000
MATH
2000
09118
001
TuTh 9:10a - 10:25a
202 Barnard Hall
Th 9:00a - 12:00p
202 Barnard Hall
D. McDuff 33 / 30 [ More Info ]

MATH BC2001x Perspectives in Mathematics 1 pt. Prerequisites: Some calculus or permission of the instructor.

Intended as an enrichment to the mathematics curriculum of the first two years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics.
Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH BC2001
MATH
2001
06129
001
W 6:10p - 7:25p
202 Milbank Hall
D. McDuff 13 / 20 [ More Info ]

MATH BC2006y Combinatorics 3 pts.Not offered in 2009-2010. Corequisites: MATH V2010 is helpful as corequisite, not required. Honors-level introductory course in enumerative combinatorics. Pigeonhole principle, binomial coefficients, permutations and combinations. Polya enumeration, inclusion-exclusion principle, generating functions and recurrence relations.

MATH V2010x or y Linear Algebra 3 pts. Prerequisites: V1201, or the equivalent. Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V2010
MATH
2010
51847
001
MW 9:10a - 10:25a
203 Mathematics Building
W 9:00a - 12:00p
203 Mathematics Building
W. Zheng 44 / 100 [ More Info ]
MATH
2010
56596
002
TuTh 6:10p - 7:25p
207 Mathematics Building
Tu 7:10p - 10:00p
207 Mathematics Buildin
E. Stein 98 / 100 [ More Info ]
MATH
2010
62050
003
MW 6:10p - 7:25p
312 Mathematics Building
M 7:10p - 10:00p
420 Pupin Laboratories
L. Huang 33 / 100 [ More Info ]
Spring 2010 :: MATH V2010
MATH
2010
78196
001
MW 9:10a - 10:25a
312 Mathematics Building
V. Pilloni 52 / 100 [ More Info ]
MATH
2010
83047
002
MW 1:10p - 2:25p
312 Mathematics Building
V. Pilloni 92 / 100 [ More Info ]
MATH
2010
64698
003
TuTh 9:10a - 10:25a
417 Mathematics Building
Y. Kerzhner 14 / 64 [ More Info ]

MATH V2020x Honors Linear Algebra 3 pts. Prerequisites: Math V1201 A more extensive treatment of the material in Math V2010, with increased emphasis on proof. Not to be taken in addition to Math V2010 or Math V1207-V1208.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V2020
MATH
2020
02902
001
MW 1:10p - 2:25p
202 Milbank Hall
D. Thurston 7 / 62 [ More Info ]

MATH V2500x or y Analysis and Optimization 3 pts. Prerequisites: Math V1102-Math V1201 or the equivalent and MATH V2010. Mathematical methods for economics. Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus of variations and optimal control. (SC)

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V2500
MATH
2500
80899
001
MW 9:10a - 10:25a
417 Mathematics Building
W 9:00a - 12:00p
417 Mathematics Building
H. Pinkham 35 / 64 [ More Info ]
Spring 2010 :: MATH V2500
MATH
2500
69261
001
MW 1:10p - 2:25p
207 Mathematics Building
M. Lipyanskiy 71 / 104 [ More Info ]

MATH V3007y Complex Variables 3 pts. Prerequisites: MATH V1202. An elementary course in functions of a complex variable. Fundamental properties of the complex numbers, differentiability, Cauchy-Riemann equations. Cauchy integral theorem. Taylor and Laurent series, poles, and essential singularities. Residue theorem and conformal mapping.(SC)

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH V3007
MATH
3007
79282
001
MW 4:10p - 5:25p
203 Mathematics Building
P. Gallagher 48 / 64 [ More Info ]

MATH V3020x Number Theory and Cryptography 3 pts. Prerequisites: one year of calculus. Congruences. Primitive roots. Quadratic residues. Contemporary applications.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V3020
MATH
3020
82546
001
MW 9:10a - 10:25a
520 Mathematics Building
W 9:00a - 12:00p
520 Mathematics Building
Y. Kerzhner 14 / 50 [ More Info ]

MATH V3021y Combinatorial Number Theory 3 pts.Not offered in 2009-2010. Prerequisites: MATH V3020 or MATH W4041. Advanced topics in number theory. Continued fractions. Approximations by rational numbers. Transcendental numbers. Arithmetic functions. Partitions of numbers and their generating functions. Stress on the combinatorial and algorithmic aspects of number theory. Contemporary applications.

MATH V3025y Making, breaking codes 3 pts.Not offered in 2009-2010. Prerequisites: Calculus I, II, III and Linear Algebra. A concrete introduction to abstract algebra. Topics in abstract algebra used in cryptography and coding theory.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH V3025
MATH
3025
23450
001
TuTh 2:40p - 3:55p
312 Mathematics Building
D. Goldfeld 72 / 100 [ More Info ]

MATH V3027x Ordinary Differential Equations 3 pts. Prerequisites: MATH V1201 or the equivalent. Corequisites: MATH V2010. Equations of order one; systems of linear equations. Second-order equations. Series solutions at regular and singular points. Boundary value problems. Selected applications.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V3027
MATH
3027
81846
001
TuTh 1:10p - 2:25p
312 Mathematics Building
P. Daskalopoulos 68 / 100 [ More Info ]

MATH V3028y Partial Differential Equations 3 pts. Prerequisites: MATH V3027 and MATH V2010 or the equivalent . Introduction to partial differential equations. First-order equations. Linear second-order equations; separation of variables, solution by series expansions. Boundary value problems.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH V3028
MATH
3028
28531
001
TuTh 1:10p - 2:25p
417 Mathematics Building
P. Daskalopoulos 61 / 64 [ More Info ]

MATH V3050y Discrete Time Models In Finance 3 pts. Prerequisites: MATH V1102, V1201(or V1101, V1102, V1201), V2010. Recommended: MATH V3027(or MATH E1210) and SIEO W3600. Elementary discrete time methods for pricing financial instruments, such as options. Notions of arbitrage, risk-neutral valuation, hedging, term-structure of interest rates.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH V3050
MATH
3050
22046
001
MW 9:10a - 10:25a
520 Mathematics Building
E. Schertzer 27 / 50 [ More Info ]

MATH V3386x Differential Geometry 3 pts. Prerequisites: MATH V1202 or the equivalent. Local and global differential geometry of submanifolds of Euclidiean 3-space. Frenet formulas for curves. Various types of curvatures for curves and surfaces and their relations. The Gauss-Bonnet theorem.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V3386
MATH
3386
82897
001
TuTh 11:00a - 12:15p
520 Mathematics Building
Tu 9:00a - 12:00p
520 Mathematics Build
R. Hamilton 28 / 50 [ More Info ]

MATH V3901x-V3902y Supervised Readings In Mathematics 2-3 pts. Prerequisites: the written permission of the staff member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the permission of the director of undergraduate studies. The written permission must be deposited with the director of undergraduate studies before registration is completed. Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V3901
MATH
3901
21950
001
TBA D. Bayer 1 [ More Info ]
MATH
3901
06431
002
TBA D. McDuff 2 [ More Info ]

MATH V3951x-V3952y Undergraduate Seminars In Mathematics 3 pts. Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the permission of the director of undergraduate studies. The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH V3951
MATH
3951
06516
001
TBA D. Bayer 19 [ More Info ]
Spring 2010 :: MATH V3952
MATH
3952
04006
001
TBA D. De Silva 20 [ More Info ]

MATH V3997x-V3998y Supervised individual research 3 pts. Prerequisites: The written permission of the faculty member who agrees to act as a supervisor, and the permission of the director of the undergraduate studies. For specially selected mathematics majors, the opportunity to write a senior thesis on a problem in contemporary mathematics under the supervision of a faculty member. .

MATH W4007y Analytic Number Theory 3 pts. Prerequisites: Math V3007 A one semeser course covering the theory of modular forms, zeta functions, L -functions, and the Riemann hypothesis. Particular topics covered include the Riemann zeta function, the prime number theorem, Dirichlet characters, Dirichlet L-functions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper half-plane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, L-functions of modular forms.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH W4007
MATH
4007
27746
001
TuTh 4:10p - 5:25p
307 Mathematics Building
P. Gallagher 11 / 18 [ More Info ]

MATH W4032y Fourier Analysis 3 pts. Prerequisites: three terms of calculus and linear algebra or four terms of calculus. Fourier series and integrals, discrete analogues, inversion and Poisson summation formulae, convolution. Heisenberg uncertainty principle. Stress on the application of Fourier analysis to a wide range of disciplines.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH W4032
MATH
4032
68746
001
MW 9:10a - 10:25a
417 Mathematics Building
N. Le 18 / 64 [ More Info ]

MATH W4041xy-W4042xy Introduction To Modern Algebra 3 pts. The second term of this course may not be taken without the first. Prerequisite: Math V1102-Math V1202 and MATH V2010, or the equivalent. Groups, homomorphisms, rings, ideals, fields, polynomials, field extensions, Galois theory.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4041
MATH
4041
01127
001
MW 2:40p - 3:55p
328 Milbank Hall
W 1:10p - 4:00p
323 Milbank Hall
W. Neumann 54 / 60 [ More Info ]
Autumn 2009 :: MATH W4042
MATH
4042
00923
001
TuTh 11:00a - 12:15p
409 Barnard Hall
Tu 9:00a - 12:00p
409 Barnard Hall
D. Bayer 16 / 60 [ More Info ]
Spring 2010 :: MATH W4041
MATH
4041
00853
001
TuTh 11:00a - 12:15p
TBA
D. Bayer 37 / 70 [ More Info ]
Spring 2010 :: MATH W4042
MATH
4042
09118
001
MW 2:40p - 3:55p
TBA
W. Neumann 31 / 70 [ More Info ]

MATH W4043y Advanced Topics In Algebra: Algebraic Number Theory 3 pts. Prerequisites: MATH W4041-W4042 or the equivalent. Algebraic number fields, unique factorization of ideals in the ring of algebraic integers in the field into prime ideals. Dirichlet unit theorem, finiteness of the class number, ramification. If time permits, p-adic numbers and Dedekind zeta function.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4043
MATH
4043
76298
001
TuTh 2:40p - 3:55p
307 Mathematics Building
Th 1:10p - 4:00p
307 Mathematics Building
K. Tignor 5 / 25 [ More Info ]

MATH W4044x Representations of Finite Groups 3 pts. Prerequisites: Math V2010 and Math W4041 or the equivalent. Finite groups acting on finite sets and finite dimensional vector spaces. Group characters. Relations with subgroups and factor groups. Arithmetic properties of character values. Applications to the theory of finite groups: Frobenius groups, Hall subgroups and solvable groups. Characters of the symmetric groups. Spherical functions on finite groups.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4044
MATH
4044
92198
001
MW 1:10p - 2:25p
520 Mathematics Building
M. Khovanov 13 / 50 [ More Info ]

MATH W4045y Algebraic Curves 3 pts. Prerequisites: Mathematics W4041,W4042 and Mathematics V3007. Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH W4045
MATH
4045
61447
001
TuTh 1:10p - 2:25p
307 Mathematics Building
A. de Jong 4 / 18 [ More Info ]

MATH W4050y Topics In Geometry and Topology 3 pts.Not offered in 2009-2010. Prerequisites: Math W4041 Advanced topics in geometry and topology chosen by the instructor from the following list. Non-Euclidean geometry (e.g., hyperbolic, elliptic, projective), combinatorial topology, algebraic topology, knot theory, braid theory, Morse theory, dynamical systems, foliations, graph theory.

MATH W4051x Topology 3 pts. Prerequisites: MATH V1202, MATH V2010, and rudiments of group theory (e.g., MATH W4041). MATH V1208 or W4061 is recommended, but not required. Metric spaces, continuity, compactness, quotient spaces. The fundamental group of topological space. Examples from knot theory and surfaces. Covering spaces.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4051
MATH
4051
76529
001
TuTh 4:10p - 5:25p
417 Mathematics Building
R. Lipshitz 24 / 62 [ More Info ]

MATH W4052x Introduction to Knot Theory 3 pts. Prerequisites: Math V2010 or equivalent and Math W4041. Recommended: Math W4051 or equivalent. The study of algebraic and geometric properties of knots in R^3, including but not limited to knot projections and Reidemeister's theorm, Seifert surfaces, braids, tangles, knot polynomials, fundamental group of knot complements. Depending on time and student interest, we will discuss more advanced topics like knot concordance, relationship to 3-manifold topology, other algebraic knot invariants.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4052
MATH
4052
84779
001
TuTh 1:10p - 2:25p
405 Mathematics Building
A. Knapp 3 / 18 [ More Info ]

MATH W4053y Introduction to Algebraic Topology 3 pts.Not offered in 2009-2010. Prerequisites: MATH V21010, MATH W4041, MATH W4051 The study of topological spaces from algebraic properties, including the essentials of homology and the fundamental group. The Brouwer fixed point theorem. The homology of surfaces. Covering spaces.

MATH W4061xy-W4062xy Introduction To Modern Analysis 3 pts. Prerequisites: The second term of this course may not be taken without the first. Prerequisites: MATH V1202 or the equivalent and V2010. Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4061
MATH
4061
25504
001
MW 11:00a - 12:15p
312 Mathematics Building
M 9:00a - 12:00p
312 Mathematics Building
O. Savin 66 / 100 [ More Info ]
Autumn 2009 :: MATH W4062
MATH
4062
48246
001
MW 11:00a - 12:15p
520 Mathematics Building
M 9:00a - 12:00p
520 Mathematics Building
I. Krichever 9 / 50 [ More Info ]
Spring 2010 :: MATH W4061
MATH
4061
02264
001
MW 1:10p - 2:25p
TBA
D. De Silva 49 / 70 [ More Info ]
Spring 2010 :: MATH W4062
MATH
4062
87546
001
MW 11:00a - 12:15p
417 Mathematics Building
O. Savin 20 / 64 [ More Info ]

MATH W4065x Honors Complex Variables 3 pts. Prerequisites: MATH V1207 and Math V1208 or MATH W4061. A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4065
MATH
4065
00789
001
MW 4:10p - 5:25p
530 Altschul Hall
D. Thurston 12 / 60 [ More Info ]

MATH W4071x Introduction To the Mathematics of Finance 3 pts. Prerequisites: MATH V1202, V3027, STAT W4150, SEIO W4150, or their equivalents. The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the BlackûScholes formula, and binomial models.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4071
MATH
4071
81279
001
MW 7:40p - 8:55p
207 Mathematics Building
W 7:10p - 10:00p
207 Mathematics Building
M. Smirnov 129 / 150 [ More Info ]

MATH W4081y Introduction To Differentiable Manifolds 3 pts. Prerequisites: MATH W4051 or W4061 and V2010. The implicit function theorem. Concept of a differentiable manifold. Tangent space and tangent bundle, vector fields, differentiable forms. Stoke's theorem, tensors. Introduction to Lie groups.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH W4081
MATH
4081
91646
001
TuTh 2:40p - 3:55p
307 Mathematics Building
M. Wang 9 / 18 [ More Info ]

MATH W4155y Probability Theory 3 pts. Prerequisites: MATH W4061 or MATH V3007. A rigorous introduction to the concepts and methods of mathematical probability starting with basic notions and making use of combinatorial and analytic techniques. Generating functions. Convergence in probability and in distribution. Discrete probability spaces, recurrence and transience of random walks. Infinite models, proof of the law of large numbers and the central limit theorem. Markov chains.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: MATH W4155
MATH
4155
66546
001
TuTh 6:10p - 7:25p
417 Mathematics Building
I. Karatzas 9 / 64 [ More Info ]

MATH W4386x-W4387y Geometrical Concepts In Physics 3 pts.Not offered in 2009-2010. Prerequisites: MATH V1202 or the equivalent and V2010. Material from topology and differential geometry with illustrations of their use in electrodynamics, general relativity, and Yang-Mills theory. In particular topological and differential manifolds, tensors, vector bundles, connections, and Lie groups are covered.

MATH W4391x-W4392y Quantum Mechanics: An Introduction for Mathematicans and Physicists 3 pts. Prerequisites: Math V1202 or the equivalent and Math V2010. This course will focus on quantum mechanics, paying attention to both the underlying mathematical structures as well as their physical motivations and consequences. It is meant for undergraduates with no previous formal training in quantum theory. The measurement problem and issues of non-locality will be stressed.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH W4391
MATH
4391
61447
001
F 1:10p - 4:00p
207 Mathematics Building
F 3:30p - 5:30p
207 Mathematics Building
B. Greene 17 / 62 [ More Info ]
Spring 2010 :: MATH W4392
MATH
4392
88346
001
F 3:30p - 5:30p
207 Mathematics Building
B. Greene 11 / 152 [ More Info ]

Engineering Courses

MATH E1210x or y Ordinary Differential Equations 3 pts. Prerequisites: MATH V1201 or the equivalent. Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH E1210
MATH
1210
27029
001
MW 1:10p - 2:25p
203 Mathematics Building
C. Virdol 38 / 100 [ More Info ]
MATH
1210
64283
002
TuTh 11:00a - 12:15p
312 Mathematics Building
Tu 9:00a - 12:00p
312 Mathematics Build
M. Wang 39 / 100 [ More Info ]
Spring 2010 :: MATH E1210
MATH
1210
62032
001
TuTh 11:00a - 12:15p
203 Mathematics Building
C. Virdol 52 / 100 [ More Info ]
MATH
1210
88448
002
TuTh 1:10p - 2:25p
207 Mathematics Building
C. Virdol 51 / 110 [ More Info ]
MATH
1210
13013
003
TuTh 4:10p - 5:25p
203 Mathematics Building
K. Tignor 26 / 110 [ More Info ]

APMA BC2001x Perspectives in Mathematics 1 pt. Prerequisites: Some calculus or permission of the instructor. Intended as an enrichment to the mathematics curriculum of the first two years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics.

MATH BC2001x Perspectives in Mathematics 1 pt. Prerequisites: Some calculus or permission of the instructor. Intended as an enrichment to the mathematics curriculum of the first two years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: MATH BC2001
MATH
2001
06129
001
W 6:10p - 7:25p
202 Milbank Hall
D. McDuff 13 / 20 [ More Info ]

APMA E4101y Introduction to nonlinear dynamical systems 3 pts. Prerequisites: MATH E1210 AND PHYS W3003. Introduction to nonlinear differential equations and dynamical systems and their chaotic behavior. Topics include Lagrangian and Hamiltonian formulation of mechanics, phase space dynamics. Critical points and stability. Systems of linear differential equations. Solving simple nonlinear differential equations. Onset of chaos. Systems with dissipation, limit points and cycles, strange attractors.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: APMA E4101
APMA
4101
86697
001
TuTh 9:10a - 10:25a
313 Fayerweather
Th 9:00a - 12:00p
313 Fayerweather
M. Weinstein 56 [ More Info ]

APMA E4101x Introduction to Dynamical Systems 3 pts. Prerequisites: APMA E2101 (or MATH E1210) and APMA E3101 An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov-Hopf; sensitive dependence and chaotic dynamics; selected applications.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: APMA E4101
APMA
4101
86697
001
TuTh 9:10a - 10:25a
313 Fayerweather
Th 9:00a - 12:00p
313 Fayerweather
M. Weinstein 56 [ More Info ]

APMA E4400y Introduction to biophysical modeling. 3 pts. Prerequisites: Advanced calculus or the instructor's approval. Introduction to physical and mathematical models of cellular and molecular biologoy. Physics at the cellular schale (viscosity, heat, diffusion, statistical mechanics). RNA transcription and regulation of genetic expression. Genetic and biochemical networks. Bioinformatics as applied to reverse-engineering of naturally-occurring networks and to forward-engineering of synthetic biological networks. Mathematical and physical aspects of functional genomics.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2010 :: APMA E4400
APMA
4400
60782
001
MW 11:00a - 12:15p
TBA
C. Wiggins 4 [ More Info ]

APMA E4901x Seminar: Problem in Applied Mathematics 1 pt. Required for all applied mathematics major in the junior year. Prerequisites or corequisites: Math V3027, V3028, and V2010, or their equivalents. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operation research, etc.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: APMA E4901
APMA
4901
78030
001
W 11:00a - 12:50p
233 Seeley W. Mudd Building
C. Wiggins 40 [ More Info ]

APMA E4903x Seminar: Problems In Applied Mathematics 3 pts. Prerequisites or corequisites: MATH V3007, V3028, and V2010, or their equivalents. Required for all applied mathematics majors in the senior year. It consists of the same weekly lecture as APMA E4901 plus two hours of tutorials per week. Examples of problem areas are nonlinear dynamics, asymptotics, approximation theory, numerical methods, etc.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2009 :: APMA E4903
APMA
4903
83032
001
M 11:00a - 11:50a
233 Seeley W. Mudd Building
W 11:00a - 11:50a
TBA
C. Wiggins 33 [ More Info ]

Of Related Interest

Computer Science

W3203 Discrete Mathematics: Introduction To Combinatorics and Graph Theory

W3251 Computational Linear Algebra

W4203 Graph Theory


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